Pixel 6 here, Android Auto stopped loading for me yesterday, was working fine before. I have a 2008 Volkswagen Rabbit with RCD360 head unit. I have tried several different cables, tried disabling and re-enabling the Android Auto app, clearing cache and user data, all to no avail. When I plug my phone in I  can see that it is trying to connect but after a few seconds I get a message notifying that the device is not compatible with Android Auto.

It's unfortunate that this problem has popped up for so many after the new release. Hopefully it gets fixed in a timely manner. For now I have to use bluetooth which isn't so bad but it's much easier to use AA.

As a side note my Pixel 6 has been giving me problems over the past few months. Not sure if this is related to the Android Auto issue, but my Pixel 6 likes to drop connection often and a restart is required to get it back together. It's very irritating especially when driving and using Android Auto. Was considering a trade-in but no carriers seem to even want this phone to trade for some reason. Anyway I hope things get ironed out. It was a good phone for a while but all the issues are starting to pile up and make for a sour experience.

update - Jimmy's suggestion worked to help me get connected for a bit, then I get disconnected because the car's clock doesnt match EXACTLY with my phone's, giving me an error message, which is kinda annoying. With my Pixel 4a the clocks could be mismatched by a couple minutes and it would still work fine.

I also noticed that maps no longer gives alternate route alerts for time saving routes after I switched to the new Android Auto UI. Hopefully this issue gets resolved.